Whakaoti i te 3y^3-7y^2+4=0

$$3 y ^ { 3 } - 7 y ^ { 2 } + 4 = 0$$

Whakaoti mō y

$$y=1$$

$$y=2$$

$$y=-\frac{2}{3}\approx -0.666666667$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 4, ā, ka wehea e q te whakarea arahanga 3. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{4}{3},±4,±\frac{2}{3},±2,±\frac{1}{3},±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$y=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te y-k o te pūrau mō ia pūtake k. Whakawehea te 3y^{3}-7y^{2}+4 ki te y-1, kia riro ko 3y^{2}-4y-4. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$3y^{2}-4y-4=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 3 mō te a, te -4 mō te b, me te -4 mō te c i te ture pūrua.

$$y=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Mahia ngā tātaitai.

$$y=\frac{4±8}{6}$$

Whakaotia te whārite 3y^{2}-4y-4=0 ina he tōrunga te ±, ina he tōraro te ±.

$$y=-\frac{2}{3} y=2$$

Rārangitia ngā otinga katoa i kitea.

$$y=1 y=-\frac{2}{3} y=2$$